Effect of a free surface on quantum wire stability

2 Effect of a free surface on quantum wire stability 

Based on the study of the buried wire in Section 6.6.1, it is clear that the critical thickness condition in this case will again have the form (6.61) where I w/h, a) is a dimensionless factor depending only on the aspect ratio w/h, and the angle a. As before, the factor /( ) incorporates the complexity of the geometry of the structure. 

The same general approach can be followed for more complex configurations. The most significant additional difficulty encountered is that neither the stress analysis problem for the background mismatch field nor that for the work of formation of the dislocation is mathematically tractable in most cases. Consequently, both and must be determined by numerical calculation. A situation of this kind of practical interest is described next. 

The pair of dislocations in problem (b) induces a traction distribution Tf- along the surface which coincides in position with the free surface in the 

These results can be compared to the critical mismatch strain results for a buried wire of height h and for a uniformly strained layer of thickness h. It is found that the critical mismatch strain for the quantum wire is approximately 20% of the critical mismatch for the corresponding buried wire and about 250% of the critical mismatch strain for a uniform layer. Therefore, much of the advantage seen for the case of a buried or completely confined wire in Section 6.6.2 is lost when the wire is in a configuration with a free surface. This observation emphasizes the importance of preventing dislocation nucleation in the structures at this critical juncture in their fabrication  

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